Question: The arithmetic sequence $(a_i)$ is defined by the formula: $a_1 = -6$ $a_i = a_{i-1} + 3$ What is $a_{7}$, the seventh term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-6$ and the common difference is $3$ To find the seventh term, we can rewrite the given recurrence as an explicit formula. The general form for an arithmetic sequence is $a_i = a_1 + d(i - 1)$ . In this case, we have $a_i = -6 + 3(i - 1)$ To find $a_{7}$ , we can simply substitute $i = 7$ into the our formula. Therefore, the seventh term is equal to $a_{7} = -6 + 3 (7 - 1) = 12$.